AP® Calculus AB-BC

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Moderate

Interval of Convergence for a Geometric Series

APCALC-TYJO4Q

Find all values of $x$ for which the given series converges:

$$\sum _{ n=0 }^{ \infty }{ 5 } { \left( \frac { x-2 }{ 3 } \right) }^{ n }$$

A

$- 3< x < 7$

B

$1 < x < 3$

C

$ -1 < x < 5 $

D

$ \cfrac{7}{5} < x < \cfrac{13}{5} $